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IBMathsDPAnalysis & Approaches (AA)SLRevision Notes2. FunctionsQuadratic Functions & GraphsSolving Quadratic Equations

Solving Quadratic Equations (DP IB Analysis & Approaches (AA)): Revision Note

Dan Finlay

Written by: Dan Finlay

Reviewed by: Jamie Wood

Updated on

DP Analysis & Approaches (AA): SLDP Analysis & Approaches (AA): HL

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Solving Quadratic Equations

How do I decide the best method to solve a quadratic equation?

  • A quadratic equation is of the form a x squared plus b x plus c equals 0

  • If it is a calculator paper then use your GDC to solve the quadratic

  • If it is a non-calculator paper then

    • you can always use the quadratic formula

    • you can factorise if it can be factorised with integers

    • you can always complete the square

How do I solve a quadratic equation by the quadratic formula?

  • If necessary rewrite in the form a x squared plus b x plus c equals 0

  • Identify the values of a, b, and c

  • Substitute the values into the formula

    • x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction 

    • This is given in the formula booklet

  • Simplify the solutions if possible

Worked Example

Solve 7 minus 3 x minus 5 x squared equals 0.

2-2-3-ib-aa-sl-quadratic-equations-c-we-solution

Examiner Tips and Tricks

When using the quadratic formula with awkward values or fractions you may find it easier to deal with the " b squared minus 4 a c " (discriminant) first. This can help avoid numerical and negative errors, improving accuracy.

How do I solve a quadratic equation by factorising?

  • Factorise to rewrite the quadratic equation in the form a left parenthesis x minus p right parenthesis left parenthesis x minus q right parenthesis equals 0

  • Equate each factor to zero and solve

    • x minus p equals 0 space rightwards double arrow space x equals p

    • x minus q equals 0 space rightwards double arrow space x equals q

Worked Example

Solve 4 x squared plus 4 x minus 15 equals 0.

2-2-3-ib-aa-sl-quadratic-equations-a-we-solution

How do I solve a quadratic equation by completing the square?

  • Complete the square to rewrite the equation in the form a open parentheses x minus h close parentheses squared plus k equals 0

  • Isolate the squared term

    • open parentheses x minus h close parentheses squared equals negative k over a

  • If open parentheses negative k over a close parentheses is negative then there will be no solutions

  • If open parentheses negative k over a close parentheses is positive then there will be two values for open parentheses x minus h close parentheses

    • x minus h equals plus-or-minus square root of negative k over a end root

  • Solve for x

    • x equals h plus-or-minus square root of negative k over a end root

Worked Example

Solve 3 x squared plus 12 x minus 5 equals 0.

2-2-3-ib-aa-sl-quadratic-equations-b-we-solution

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    Author
    Reviewer
    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

    Jamie Wood

    Reviewer: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.